Opacity Correction
In the quality laboratory of a modern paper mill, color, brightness, whiteness, and fluorescence of the product are conventionally measured on a multiple sheet "pad" of the paper, rather than on a single sheet. If only a single sheet is measured, the results will be influenced by both the partial transparency of the sheet and the reflectance of the backing against which the sheet is observed. Furthermore, the "infinite pad" value is usually what the end customer is concerned with, since this is typically how the customer will view the end product. However, these measurement conditions cannot be reproduced in-situ in the manufacturing process, where an "on-line" color sensor can view only a single thickness of the product.
Two strategies have been employed to improve the agreement of on-line color measurements with laboratory "pad" measurements. The first strategy, an example of which is disclosed in U.S. Pat. No. 4,715,715, is to back the sheet with an opaque material which approximates the color and optical scattering power of the paper being manufactured. In effect, this strategy reproduces infinite pad conditions. The measurement error at each wavelength will be proportional to the mismatch between artificial and real "pad" spectral reflectance and inversely proportional to the square of the spectral transmittance of the single sheet. This strategy works well for sheets of medium to low transparency (&lt;20%), since only modest agreement between backing and product is required. For less opaque paper or in the case of frequently changing product targets it is often difficult to keep the backing in close enough agreement with the product to insure good sensor performance.
The second strategy is to measure the sheet spectral reflectivity twice, once backed with a highly reflective (i.e., "white") material, and once backed with a highly absorptive (i.e., "black") material. From these independent measurements, the spectral transparency can be determined and the infinite pad spectral reflectivity calculated according to the Kubelka-Munk theory. An example of an apparatus for measuring dark and bright reflectances in succession is disclosed in U.S. Pat. No. 4,944,594. The apparatus of that patent includes a sheet backing system comprising an optical gating means that absorbs substantially all of the transmitted portion of the incident radiation when electronically switched to a dark state and reflects substantially all of the transmitted portion of the radiation when switched to a bright state. This approach does not require maintenance of product related backings and is therefore to be generally preferred. However, if the two measurements occur at significantly different times on significantly different parts of the paper, then the difference between the "black backed" and "white backed" spectral reflectivities may be due not only to the transparency of the sheet but to product (color and transparency) non-uniformity as well. If such variations are present, the calculation under the Kubelka-Munk theory will fail. On a modern paper machine, the web travels at 50 feet per second or more, and the sensor itself may be on a scanner moving 15 inches per second across the traveling sheet. In accordance with systems of the prior art in which the backing must be switched from "black" to "white" between these measurements, the measurements will thus inevitably be made on very different parts of the sheet. In these systems, the results of numerous reading sequences are typically combined in an attempt to average out the effect of product color non-uniformity. The final measurement update rate is then necessarily low and does not permit accurate, rapid control of color during fabrication of the paper.
Attempts have been made to make simultaneous "black" and "white" backed measurements. For example, U.S. Pat. No. 3,936,189 discloses a tristimulus colorimeter for on-line monitoring of the color, opacity and brightness of a moving web such as paper having an area illuminated by a light source. The colorimeter of the '189 patent includes four photometers each incorporating a filter to duplicate the ICI tristimulus functions for measuring the tristimulus values of the light incident on these detectors; a brightness detector having a 457 nm filter (brightness, according to the '189 patent, being defined as reflectance at a source wavelength of 457 nm); and an opacity detector fitted with a Y response filter. The '189 patent further includes a sheet backing element including a quartz "shoe" providing both black and white backgrounds. The black background is provided by a cavity under the quartz shoe while the white background is provided by a white stripe on the surface of the shoe. The photometers are so oriented that the optical axes of the four color tristimulus value detectors and the brightness detector are directed toward a portion of the illuminated area overlying the black background while the optical axis of the opacity detector is directed towards a portion of the illuminated area overlying the white stripe. The output of the opacity detector and the output of the tristimulus value detector providing the tristimulus Y measurement are used to provide a value of contrast ratio reflectance for correcting color luminosity or brightness to infinite pad backing. However, because the sensor of the '189 patent employs an opacity correction strategy that only corrects for one of the three color coordinates which is insufficient to fully define a color, a true color correction can only be estimated. Except for neutral colors, even the Y correction is in error since the Y-value is a weighted average over a wavelength band and the transparency correction is a non-linear function of "black" and "white" backed reflectivities which must be applied at each wavelength before computing the Y-value.
Accordingly, instead of simply a calculation of the luminosity or brightness of the sheet for infinite backing, what is needed is a wavelength-by-wavelength opacity correction before computing all color coordinates, that is, a full color correction for opacity at every wavelength. Moreover, such correction should be made in real time to permit immediate on-line adjustments to be made in the papermaking process.